pub fn new_birthday_probability(n: u32) -> f64 {
    if n < 2 {
        return 0.0;
    }

    let days_in_year = 365;
    let prob: f64 = (0..n)
        .map(|i| (days_in_year - i) as f64 / days_in_year as f64)
        .product();
    1.0 - prob
}
